The Legend of Srinivasa Ramanujan

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In 1913, a young man from the city of Madras in British India sent a letter to one of the world’s preeminent mathematicians, G.H. Hardy, in Cambridge Univerisity in England. 

The young man had no formal education in advanced mathematics, yet that letter would end up changing the landscape of mathematics for the rest of the 20th century. 

Learn more about the legendary Srinivasa Ramanujan, one of the world’s most gifted natural mathematicians, on this episode of Everything Everywhere Daily. 

On December 22, 1887, Srinivasa Ramanujan was born into a brahmin family in what is today the southern Indian state of Tamil Nadu. 

His father was a clerk who spent much of his time working to support his family. 

His mother, who was a devout Hindu, brought him up and passed along her religious devotion to her son. 

While he didn’t enjoy his first attempts at school, he eventually excelled. At the age of 10, he had passed his primary school exams with the highest score in his district. He was advanced to secondary school, where it soon became evident he was a prodigy. 

By the age of 11, he had exhausted the two university students who were renting a room from his family.  He was given a book on trigonometry, which he taught himself and had fully completed by the age of 13. 

When he was 16 he was given a copy of A Synopsis of Elementary Results in Pure and Applied Mathematics, by British mathematician G. S. Carr which was a collection of over 5,000 mathematical theorems.

It was with this book, that Ramanujan came into his own. He began developing his own theorems and coming up with his own unique solutions to problems. 

In 1904 he graduated high school and was given a special prize for excellence in mathematics. He easily got a scholarship to attend a nearby college. 

As brilliant as he was, however, he had absolutely no interest in anything other than mathematics. He failed his other subjects as he had no interest in them, and eventually, his scholarship was revoked. 

He attended university again, only to suffer the same problem. Extreme interest in mathematics, and zero interest in anything else. Even in mathematics, he only bothered with questions that interested him and didn’t bother with things he found easy. 

After failing to get a degree, he lived in poverty, near starving, working on mathematics independently. 

In 1910 he began to make contacts in the Indian mathematical world. Some of them, including the head of the Indian Mathematica Society, didn’t believe that his work was his own. 

He eventually contacted V. Ramaswamy Aiyer who was the founder of the Indian Mathematical Society. He also worked at the department of revenue, where Ramanujan wanted to get a job. 

He looked at Ramanujan’s work and said:

I was struck by the extraordinary mathematical results contained in [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department.

Eventually, the mathematicians in India came to terms with his brilliance and originality and he was given a job as a clerk where he earned a decent salary.

From here, Ramanujan, with the help of other Indian mathematicians, tried to get the attention of mathematicians in Britain. Papers showing his theorems and ideas were sent to many high-profile mathematicians, but none of them took an interest. Either they felt he was too undisciplined, or they ignored what was sent to them entirely.

However, there was one letter sent in January of 1913 to one G.H. Hardy of Cambridge University. Many notable mathematicians and scientists will often get letters from cranks with crackpot ideas, so it wasn’t too surprising that Ramanujan didn’t get attention at first.

His letter to Hardy began:

Dear Sir, 

I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age. I have had no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling”.

From here, Ramanujan proceeded to outline many of his theorems over the course of 12 pages. 

Hardy was blown away. To be fair, some of Ramanujan’s ideas were not original and had been discovered before, but the vast majority were grounding breaking. 

Hardy said in a reply letter:

Certainly the most remarkable [letter] I have ever received, its author a mathematician of the highest quality, a man of altogether exceptional originality and power.

One of the problems was that Ramanujan was mostly self-taught. Mathematics is built upon formal proofs, and Ramanujan’s work wasn’t done that way. It was mostly intuitive just springing fully formed from his mind. 

Hardy wanted Ramanujan to come to England to study, but his parents provided resistance. Eventually, they relented, and in 1914 Ramanujan headed to England.

He spent 5 years there with Hardy and other mathematicians working on proving his theorems and publishing them to the outside world. 

His relationship with Hardy was perhaps the most famous between any two mathematicians in history. They couldn’t have been more unalike. Ramanujan was deeply spiritual, whereas Hardy was an atheist. Hardy was classically trained, whereas Ramanujan was high intuitive. Hardy was English and Ramanujan was Indian. 

Over time, the entire mathematical community came to recognize his genius. Cambridge awarded him a Bachelor of Arts by Research degree, which was the precursor to the Ph.D. 

In 1917 he was elected to the London Mathematical Society. In 1918, he was elected a Fellow of the Royal Society, only the second Indian to receive the honor and at the age of 31, he was one of the youngest fellows in the history of the Royal Society. He was also the first Indian elected to be a fellow of Trinity College. 

To give you just a small glimpse of his brilliance, once he was sick and Hardy came to visit him. He wrote later on:

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No”, he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”

This off-handed comment made while he was sick about a single number, 1729, it today known as the Hardy–Ramanujan number, and there is now an entire classification of numbers called Taxicab numbers, numbers that are the sum of two cubes in two different ways.

Ramanujan’s theorems and conjectures spread over a wide range of mathematics which is still having an impact today. His work on elliptic curves was a big part of the basis for proving Fermat’s Last Theorem.  He’s also had a staggering impact on areas such as elliptic functions, continued fractions, and infinite series. He found an infinite series to approximate the value of pi, and he cracked the problem of partitions, which was thought to be impossible.

Ramanujan suffered from illness even before he came to England, and the cold damp climate of the country didn’t help things. As a strict vegetarian, he found it difficult to find fresh vegetables during WWI, and he suffered from tuberculosis and various nutrient deficiencies. 

In 1919, after the conclusion of the war, he returned to India and died in 1920 at the age of 32. 

The legacy of Ramanujan continued well after his death. The majority of his conjectures that he postulated have since been proven true.

In 1976, a lost notebook of work which he completed during the last year of his life was found, and it was likened to finding Beethoven’s 10th Symphony. 

His birthday, December 22, is now National Mathematics day in India. 

The Ramanujan IT zone is a special economic zone in Chennai, India.

He has appeared on postage stamps, and his story was documented in the 2015 film, the Man Who Knew Infinity starring Dev Patel and Jeremy Irons. 

After Ramanujan’s death, Hardy ranked the mathematicians of his time on a scale of 1 to 100. He placed himself at 25, his colleague J. E. Littlewood at 30, the great German mathematician David Hilbert at 80, and Ramanujan at a perfect 100.